Martin Allen's side made a nervous start to the game but took an early lead through Byrne's free-kick, which deflected off the wall and left Burton goalkeeper Ross Atkins wrong-footed.
The Great Escape - again
Barnet have taken their battle against relegation from the Football League to the final day for each of the last three years - and survived each time
The home side were soon back on level terms though, with Maghoma sending a low drive into the bottom corner after linking with Zola on the edge of the area.
Zola could have given Burton the lead from the penalty spot after he was pushed over by Byrne, however, he blazed his effort wildly over the bar.
With Hereford leading against Torquay it looked as though Barnet were heading for relegation. However, captain Hughes squeezed home a left-footed volley to put his side back into the lead, before goalkeeper Dean Brill denied Patrick Ada an equaliser in injury time.
VIEWS FROM THE DRESSING ROOM
Burton Albion caretaker manager Gary Rowett told BBC Radio Derby:
"I felt that in the first half we played some quite nice football.
"They obviously wanted it more than us, had that little bit of desire, and I'm disappointed that it was another not great performance.
"I have to look over the last 10 games and say that we have achieved something, we've won three games when we couldn't win a single one. I have to take the positives."
Barnet manager Martin Allen told BBC London 94.9:
"It was a nervy afternoon, we didn't play that well in the first half but that was to be expected with the tension and anxiety throughout the week.
"The second half we played really well, we really stepped up to the mark and full credit to the players for that performance.
"That was total domination, it was really just a matter of time.
"Their were two penalties that didn't go our way but the captain got the fantastic shot and we got a deserved three points.
Full Time The final whistle is blown by the referee.
Inswinging corner taken by Chris Palmer.
Chris Palmer takes the inswinging corner, Patrick Ada takes a shot. Save by Dean Brill.
Inswinging corner taken left-footed by Chris Palmer from the right by-line, clearance by Jordan Mustoe.
Unfair challenge on Izale McLeod by Ross Atkins results in a free kick. Direct free kick taken by Jordan Mustoe.
Ben May produces a cross, Ross Atkins makes a save.
Nathan Stanton gives away a free kick for an unfair challenge on Ben May. Direct free kick taken by Michael Hector.
A cross is delivered by Ricky Holmes.
Free kick awarded for an unfair challenge on Ricky Holmes by Andrew Corbett. Mark Byrne takes the free kick.
Michael Hector gives away a free kick for an unfair challenge on Jimmy Phillips. Chris Palmer delivers the ball from the free kick right-footed from left channel, save by Dean Brill.
Izale McLeod produces a left-footed shot from inside the six-yard box that clears the bar.
Booking Nathan Stanton goes into the referee's book.
Booking Booking for Izale McLeod for unsporting behaviour.
Izale McLeod challenges Nathan Stanton unfairly and gives away a free kick. Ross Atkins takes the free kick.
Foul by Calvin Zola on Clovis Kamdjo, free kick awarded. Dean Brill takes the direct free kick.
Ricky Holmes takes a shot. Save made by Ross Atkins.
Mark Byrne takes the inswinging corner, Ross Atkins makes a save.
Substitution Jimmy Phillips is brought on as a substitute for Adam Bolder.
Izale McLeod has an effort at goal from long distance that misses to the right of the goal.
Effort on goal by Jacques Maghoma from long range goes harmlessly over the target.
Corner taken left-footed by Jordan Mustoe from the right by-line, save by Ross Atkins.
Mark Byrne has an effort at goal from just outside the box which goes wide of the left-hand upright.
Unfair challenge on Jordan Mustoe by Jacques Maghoma results in a free kick. Direct free kick taken by Jordan Mustoe, Effort on goal by Mark Byrne from outside the box goes harmlessly over the bar.
Direct free kick taken by Mark Byrne.
Substitution (Burton Albion) makes a substitution, with Greg Pearson coming on for Cleveland Taylor.
Foul by Andrew Corbett on Ricky Holmes, free kick awarded.
Booking Calvin Zola goes into the book for unsporting behaviour.
Calvin Zola concedes a free kick for a foul on Dean Brill. Dean Brill takes the free kick.
Chris Palmer takes a shot. Clovis Kamdjo gets a block in.
59:53 Goal scored
Goal! - Mark Hughes - Burton 1 - 2 Barnet Goal scored by Mark Hughes from just outside the area to the bottom left corner of the goal. Burton Albion 1-2 Barnet.
Mark Byrne takes a shot. Blocked by Nathan Stanton.
Ben May fouled by Nathan Stanton, the ref awards a free kick. Jordan Mustoe takes the direct free kick.
Sam Deering challenges Chris Palmer unfairly and gives away a free kick. Ross Atkins takes the direct free kick.
Ricky Holmes crosses the ball.
Cleveland Taylor takes a shot. Blocked by Clovis Kamdjo.
Izale McLeod challenges Nathan Stanton unfairly and gives away a free kick. Ross Atkins restarts play with the free kick.
Close range shot by Sam Deering goes wide of the left-hand post.
Booking Mark Byrne booked.
Ricky Holmes takes a shot. Blocked by Patrick Ada.
The offside flag is raised against Izale McLeod. Ross Atkins restarts play with the free kick.
Ben May produces a left-footed shot from the edge of the box and misses to the left of the goal.
A cross is delivered by Jack Dyer, clearance made by Jack Saville.
Chris Palmer takes the inswinging corner, save by Dean Brill.
The second half has started.
Substitution (Barnet) makes a substitution, with Izale McLeod coming on for Scott McGleish.
45:00 +2:12 Half time
Half Time The referee calls an end to the first half.
45:00 +1:43 Booking
Booking Booking for Chris Palmer for unsporting behaviour.
Chris Palmer concedes a free kick for a foul on Sam Deering. Direct free kick taken by Jordan Mustoe.
Free kick awarded for an unfair challenge on Andrew Corbett by Ricky Holmes. Free kick taken by Ross Atkins.
Penalty taken by Calvin Zola and missed.
Penalty awarded for a foul by Mark Byrne on Calvin Zola.
Ricky Holmes crosses the ball.
The ball is swung over by Ricky Holmes, Andrew Corbett manages to make a clearance.
Mark Byrne fouled by Adam Bolder, the ref awards a free kick. Mark Byrne takes the free kick.
Chris Palmer crosses the ball, clearance by Clovis Kamdjo.
Foul by Michael Hector on Cleveland Taylor, free kick awarded. Free kick taken by Jack Dyer.
Inswinging corner taken by Jordan Mustoe.
Calvin Zola fouled by Clovis Kamdjo, the ref awards a free kick. Chris Palmer takes the direct free kick.
Ricky Holmes produces a right-footed shot from just outside the penalty box that goes wide left of the target.
Adam Bolder takes a shot. Save by Dean Brill.
The assist for the goal came from Calvin Zola.
26:09 Goal scored
Goal! - Jacques Maghoma - Burton 1 - 1 Barnet A goal is scored by Jacques Maghoma from the edge of the area to the bottom right corner of the goal. Burton Albion 1-1 Barnet.
Centre by Sam Deering.
Jack Dyer produces a cross, clearance by Clovis Kamdjo.
Chris Palmer has an effort at goal from outside the penalty box which goes wide left of the goal.
Calvin Zola takes a shot. Save by Dean Brill.
Patrick Ada fouled by Ricky Holmes, the ref awards a free kick. Nathan Stanton restarts play with the free kick.
Jordan Mustoe challenges Cleveland Taylor unfairly and gives away a free kick. Ross Atkins takes the direct free kick. The ball is swung over by Andrew Corbett, clearance made by Clovis Kamdjo. Inswinging corner taken from the right by-line by Chris Palmer.
Jacques Maghoma challenges Scott McGleish unfairly and gives away a free kick. Michael Hector takes the free kick.
Effort on goal by Jack Dyer from just inside the area clears the crossbar.
Scott McGleish challenges Nathan Stanton unfairly and gives away a free kick. Free kick taken by Ross Atkins.
Free kick awarded for an unfair challenge on Jack Saville by Calvin Zola. Direct free kick taken by Dean Brill.
Chris Palmer takes a inswinging corner to the near post.
Corner taken by Chris Palmer.
Assist by Jordan Mustoe.
5:48 Goal scored
Goal! - Mark Byrne - Burton 0 - 1 Barnet Mark Byrne fires in a goal from just outside the penalty box to the bottom right corner of the goal. Burton Albion 0-1 Barnet.
Unfair challenge on Mark Hughes by Adam Bolder results in a free kick. Free kick taken by Jordan Mustoe,
Corner from the right by-line taken by Chris Palmer, save made by Dean Brill.
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